A solid metal sphere has a mass of 11.7 kg and a radius of 23.5 cm. In iron rod pierces the sphere through its diameter. The rod has a mass of 4.80 kg and a total length of 80.0 cm. Two little rockets are pushing perpendicular to the ends of the rods as shown, each with a force of 6.80 Newtons, causing the whole thing to spin. (a) Find the total moment of inertia, I, of the sphere-rod combination. (b) Find the angular acceleration of the system.
A solid metal sphere has a mass of 11.7 kg and a radius of 23.5 cm. In iron rod pierces the sphere through its diameter. The rod has a mass of 4.80 kg and a total length of 80.0 cm. Two little rockets are pushing perpendicular to the ends of the rods as shown, each with a force of 6.80 Newtons, causing the whole thing to spin. (a) Find the total moment of inertia, I, of the sphere-rod combination. (b) Find the angular acceleration of the system.
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![A solid metal sphere has a mass of 11.7 kg and a radius of 23.5 cm. In iron rod
pierces the sphere through its diameter. The rod has a mass of 4.80 kg and a
total length of 80.0 cm. Two little rockets are pushing perpendicular to the ends
of the rods as shown, each with a force of 6.80 Newtons, causing the whole
thing to spin.
(a) Find the total moment of inertia, I, of the sphere-rod combination.
(b) Find the angular acceleration of the system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff456c65b-f482-4083-8c37-6fe7d8344e1a%2F774cb2c7-41dd-488c-9e66-813970082c98%2Fh0k61qr_processed.png&w=3840&q=75)
Transcribed Image Text:A solid metal sphere has a mass of 11.7 kg and a radius of 23.5 cm. In iron rod
pierces the sphere through its diameter. The rod has a mass of 4.80 kg and a
total length of 80.0 cm. Two little rockets are pushing perpendicular to the ends
of the rods as shown, each with a force of 6.80 Newtons, causing the whole
thing to spin.
(a) Find the total moment of inertia, I, of the sphere-rod combination.
(b) Find the angular acceleration of the system.
![FORMULAS
s= r0,
1= lever arm
T = FI, where
v = ro,
Torque: t = F(sin0)r
a = ra
Equilibrium: Στ-0
Non-equilibrium:
Στ= Ια
Moments of Inertia for Various Rigid Objects of uniform composition: Point
mass: I= MR2
Moments of Inertia for Various Rigid Objects of Uniform Composition
Hoop or thin
cylindrical shell
1= MR
Solid sphere
R
Solid cylinder
or disk
Thin spherical
shell
-MR
2
MR
1=-
2
Long, thin rod
with rotation axis
through center
I MI?
Long, thin
rod with
rotation axis
through end
ML?
= r®,
1= lever arm
v = ro,
a = ra
Torque: t = F(sin0)r
T = Fl, where
%3D
Equilibrium: Στ-0
Non-equilibrium:
Στ-Ια](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff456c65b-f482-4083-8c37-6fe7d8344e1a%2F774cb2c7-41dd-488c-9e66-813970082c98%2Fp3wl7uu_processed.png&w=3840&q=75)
Transcribed Image Text:FORMULAS
s= r0,
1= lever arm
T = FI, where
v = ro,
Torque: t = F(sin0)r
a = ra
Equilibrium: Στ-0
Non-equilibrium:
Στ= Ια
Moments of Inertia for Various Rigid Objects of uniform composition: Point
mass: I= MR2
Moments of Inertia for Various Rigid Objects of Uniform Composition
Hoop or thin
cylindrical shell
1= MR
Solid sphere
R
Solid cylinder
or disk
Thin spherical
shell
-MR
2
MR
1=-
2
Long, thin rod
with rotation axis
through center
I MI?
Long, thin
rod with
rotation axis
through end
ML?
= r®,
1= lever arm
v = ro,
a = ra
Torque: t = F(sin0)r
T = Fl, where
%3D
Equilibrium: Στ-0
Non-equilibrium:
Στ-Ια
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